SOLUTION: If two cars start driving in the same direction from the same place, while one is traveling 45 mph and the other 50 mph, how long will it take them to be 30 miles apart? I've do

Question 91536: If two cars start driving in the same direction from the same place, while one is traveling 45 mph and the other 50 mph, how long will it take them to be 30 miles apart?
I've done this problem 2 ways and both ways gives me the answer, but they are actually reversed.
First way: 45(x+30) = 50x Answer: x = 270, x+30 = 300
Seconc way: 45x = 50(x-30) Answer: x = 300, x-30 = 270
when completed: 270/45 = 6 and 300/50 = 6
However, the two ways I've done this problem I can't get 6 because 270 and 300 are matched with the incorrect variable.
HELP....PLEASE, what have I done incorrectly??

Answer by stanbon(48554) (Show Source):
You can put this solution on YOUR website!
If two cars start driving in the same direction from the same place, while one is traveling 45 mph and the other 50 mph, how long will it take them to be 30 miles apart?
Comment: There are really two solutions as the faster car is 30 miles short
of the slower car and later it is 30 beyond the slower car. I'm going to
work the latter case.
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1st car DATA:
distance = x miles ; rate = 45 mph; time = d/r = x/45
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2nd car DATA:
distance = x+30 miles ; rate = 50 mph; time = d/r = (x+30)/50
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EQUATION:
time = time
x/45 = (x+30)/50
50x = 45x+1350
5x = 1350
x = 270 miles
x/45 = 6 hrs (the faster car will be 30 miles beyond the slower car
in 6 hrs.)
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Cheers,
Stan H.